(-1)n1+n2+k1+k2 Lk1+n1,k2+n2l1-n1,l2-n2,.


We can show immediately that Eq. (REF ) includes the Onsager relation in the linear response region
as follows.
First, \(L_{l_1, l_2}^{k_1, k_2}(B)\)  are related to ordinary observables
by changing affinities to the external-bias variables,
\({\cal A}_c\)  and \({\cal A}_e\)  to
the bias voltage \(V = \mu _L - \mu _R\)  and the temperature difference \(\Delta T = T_L - T_R\) . (For example,
the linear conductance of charge current, the charge current noise at equilibrium and the Seebeck coefficient are written as
\(G = L_{1,0}^{1,0}/T\) , \(S_{I, I} = L_{0,0}^{2,0}\)  and \(S= L_{0,1}^{1,0}/ TL_{1,0}^{1,0}\) ,
respectively.)
We note that the linear response of charge and heat currents are
expressed by \(I_c = L_{1,0}^{1,0}(B) (V/T) + L_{0,1}^{1,0}(B) (\Delta T/T^2)\)  and
\(I_e = L_{1,0}^{0,1}(B) (V/T) + L_{0,1}^{0,1}(B) (\Delta T/T^2)\) . [1]}
Then, specific equations between coefficients satisfying
\(N \equiv k_1+k_2+l_1+l_2 = 2\)  lead to the Onsager relation \(L_{0,1}^{1,0}(B) = L_{1,0}^{0,1}(-B)\) .
